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ARTICLE

A Weighted Average Finite Difference Scheme for the Numerical Solution of Stochastic Parabolic Partial Differential Equations

Dumitru Baleanu1,2,3, Mehran Namjoo4, Ali Mohebbian4, Amin Jajarmi5,*
1 Department of Mathematics, Faculty of Arts and Sciences, Çankaya University, Ankara, 06530, Turkey
2 Institute of Space Sciences, Magurele-Bucharest, R 76900, Romania
3 Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, 40402, Taiwan
4 Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, 77188-97111, Iran
5 Department of Electrical Engineering, University of Bojnord, Bojnord, 94531-1339, Iran
* Corresponding Author: Amin Jajarmi. Email: a.jajarmi@ub.ac.ir

Computer Modeling in Engineering & Sciences https://doi.org/10.32604/cmes.2022.022403

Received 08 March 2022; Accepted 07 June 2022; Published online 23 June 2022

Abstract

In the present paper, the numerical solution of Itô type stochastic parabolic equation with a time white noise process is imparted based on a stochastic finite difference scheme. At the beginning, an implicit stochastic finite difference scheme is presented for this equation. Some mathematical analyses of the scheme are then discussed. Lastly, to ascertain the efficacy and accuracy of the suggested technique, the numerical results are discussed and compared with the exact solution.

Keywords

Itô equation; stochastic process; finite difference scheme; stability and convergence; consistency
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